The “Cloud Method”
Multiplication itself seems tricky, and mental math seems even harder. However, it’s certainly not impossible to work out equations in your head, and there are methods that help make the answers closer to reach. For mental multiplication, the “cloud method” helps one multiply any 2-digit number by any 2-digit number from 10 to 99 in a matter of seconds. There’s no strict name for this technique, so for this article I will be referring to it as the “cloud method” because when the method is visually drawn out it resembles a cloud. Math at its foremost is an innovative process that requires constant thinking outside of the box. Using this perspective, don’t hesitate to be creative with this one and choose a name that helps you remember and keeps math fun for you! ☁
The cloud method first begins with a pencil and practice on paper. After drawing three boxes side by side and after choosing two two-digit numbers to multiply (such as 21X21), find the product of the first digit of the first number and the first digit of the second number and write it in the first box. Then, write the product of the second digit of the first number and the second digit of the second number in the last box. Following that, in the box in the middle, write the sum of the product of the first digit of the first number and the second digit of the second number and the product of the second digit of the first number and the first digit of the second number. Finally, after removing the boxes and rewriting the numbers into a whole number you will reach the correct answer for this problem (in this case, 441)!
Another important step in understanding how this method works is by understanding how to carry over numbers from boxes with two digits in them. In the steps below, we’ll work out the example problem of 42X91.
4X9=36 • Multiply 4, the first digit of the first number, and 9, the first digit of the second number. Place the product in the first box.
2X1=2 • Multiply 2, the second digit of the first number, and 1, the second digit of the second number. Place the product in the last box.
(4X1)+(2X9)=22 • Multiply 4, the first digit of the first number, and 1, the second digit of the second number. Then multiply 2, the second digit of the first number, and 9, the first digit of the second number. Add the products and place the sum in the middle box.
36 22 2 • Put the numbers 36, 2, and 22 in their corresponding boxes (here, the double spaces between the numbers represent the boxes).
38 2 2 • Carry the 2, or the first digit in the number 22, over to 6, or the last digit in the number 36. Add the 2 to the 6 to get 38 in the first box.
3,822 • Rewrite the number into standard format.
Great job! The cloud method sounds complex, but once put into practice, this method can help you even do mental multiplication in only a few seconds. It’s all about visualization, which will get easier after a while. And this will not only help you with your homework but with many other things as well. After all, it’s usefulness is only rivaled by how fun it is to amaze your friends. ☁
